Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Homework problems

The following is a graph of the height of a water wave as a function of position, at a certain moment in time.

Trace this graph onto another piece of paper, and then sketch below it the corresponding graphs that would be obtained if

(a) the amplitude and frequency were doubled while the velocity remained the same;

(b) the frequency and velocity were both doubled while the amplitude remained unchanged;

(c) the wavelength and amplitude were reduced by a factor of three while the velocity was doubled.

[Problem by Arnold Arons.]

(a) The graph shows the height of a water wave pulse as a function of position. Draw a graph of height as a function of time for a specific point on the water. Assume the pulse is traveling to the right.

(b) Repeat part a, but assume the pulse is traveling to the left.

(c) Now assume the original graph was of height as a function of time, and draw a graph of height as a function of position, assuming the pulse is traveling to the right.

(d) Repeat part c, but assume the pulse is traveling to the left.

[Problem by Arnold Arons.]

The figure shows one wavelength of a steady sinusoidal wave traveling to the right along a string. Define a coordinate system in which the positive x axis points to the right and the positive y axis up, such that the flattened string would have y=0. Copy the figure, and label with "y=0" all the appropriate parts of the string. Similarly, label with "v=0" all parts of the string whose velocities are zero, and with "a=0" all parts whose accelerations are zero. There is more than one point whose velocity is of the greatest magnitude. Pick one of these, and indicate the direction of its velocity vector. Do the same for a point having the maximum magnitude of acceleration.

[Problem by Arnold Arons.]
4Find an equation for the relationship between the Doppler-shifted frequency of a wave and the frequency of the original wave, for the case of a stationary observer and a source moving directly toward or away from the observer.
5Suggest a quantitative experiment to look for any deviation from the principle of superposition for surface waves in water. Make it simple and practical.
6The musical note middle C has a frequency of 262 Hz. What are its period and wavelength?
7Singing that is off-pitch by more than about 1% sounds bad. How fast would a singer have to be moving relative to a the rest of a band to make this much of a change in pitch due to the Doppler effect?
8In section 3.2, we saw that the speed of waves on a string depends on the ratio of T/μ, i.e., the speed of the wave is greater if the string is under more tension, and less if it has more inertia. This is true in general: the speed of a mechanical wave always depends on the medium's inertia in relation to the restoring force (tension, stiffness, resistance to compression,...) Based on these ideas, explain why the speed of sound in a gas depends strongly on temperature, while the speed of sounds in liquids and solids does not.

Last Update: 2010-11-11